Exam_1 Oct 2007 - MVA:= 1000kW MW:= MVA MVAr:= MVA f:= 50 ⋅ Hz ω:= 2πf ω = 314.15927 Hz ΟΜΑ∆Α 1 ΘΕΜΑ 1(4 βαθµοί A:= 0.927 ⋅

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Unformatted text preview: MVA := 1000kW MW := MVA MVAr := MVA f := 50 ⋅ Hz ω := 2πf ω = 314.15927 Hz ΟΜΑ∆Α 1 ΘΕΜΑ 1ο (4 βαθµοί) A := 0.927 ⋅ e j⋅ 0.866 deg B := 151.2 ⋅ e 150 ⋅ kV ES := j⋅ 79.23 deg Ω C := 0.000944 ⋅ e j⋅ 90.277 deg ES = 86.60254 kV 3 Ax := Re( A) Ax = 0.92689 Ay := Im( A) Ay = 0.01401 Bx := Re( B) Bx = 28.25429 Ω By := Im( B) By = 148.53665 Ω a := ( B ⋅ ES ) 4 b := 2 ⋅ ( ES ) b := 2 ⋅ ( ES ) 2 ⋅ Im( A ⋅ B) c := ( 8 kg m a = 171460800000000 12 6 s A 2 3 6 3 6 ES ⋅ A ⋅ ( Bx ⋅ Ay − By ⋅ Ax) kg m b = −2059228239123.28 9 4 s A ⎯ 2 kg m b = −2059228239123.28 9 4 s A )2 − ( ES )2 2 c = −1055032500 4 kg m 6 2 s A 2 b + b − 4⋅a⋅c XL1 := 2⋅c XL1 = −79.98668 Ω 2 b − b − 4⋅a⋅c XL2 := L1 := L2 := 2⋅c XL1 L1 = −0.25461 H XL2 ω ES := ⎡A + ⎛ −B ⋅ j ⋅ ⎢ ⎜ ⎝ 1 ⎞⎤ ⋅ E S ⎥ XL1 ⎠⎦ (rejected) L2 = 6.46743 H ω ⎣ XL2 = 2031.80167 Ω (per circuit & per phase) ES = 86.60254 kV arg ( ES ) = 158.45401 deg ES := ⎡A + ⎛ −B ⋅ j ⋅ ⎢ ⎜ ⎣ ⎝ 1 ⎞⎤ ⋅ E S ⎥ XL2 ⎠⎦ ES = 86.60254 kV arg ( ES ) = 0.00599 deg S D := A ΘΕΜΑ 2o (3 βαθµοί) A1 := A B1 := B C1 := C D1 := D A2 := A1 B2 := B1 C2 := C1 D2 := D1 A := ( A1 ⋅ B2 + A2 ⋅ B1) ( B 1 + B 2) B := ( A1 − A2) ⋅ ( D2 − D1) C := C1 + C2 + B1 + B2 D := A B1 + B2 A = 0.92689 + 0.01401j B1 ⋅ B2 B = 14.12714 + 74.26832j Ω C = −0.00001 + 0.00189j S A = 0.927 arg ( A) = 0.866 deg B = 75.6 Ω arg ( B) = 79.23 deg C = 0.00189 S arg ( C) = 90.277 deg D = 0.927 arg ( D) = 0.866 deg A := A1 B := B1 2 A = 0.92689 + 0.01401j C := 2C1 D := A B = 14.12714 + 74.26832j Ω C = −0.00001 + 0.00189j S A = 0.927 arg ( A) = 0.866 deg B = 75.6 Ω arg ( B) = 79.23 deg C = 0.00189 S arg ( C) = 90.277 deg D = 0.927 arg ( D) = 0.866 deg ER := 140 ⋅ ( kV) ⋅ e j⋅ 0 3 ER = 80.82904 kV ES := 150 ⋅ ( kV) ⋅ e j⋅ 12deg 3 ES = 84.71007 + 18.00568j kV ES = 86.60254 kV ( ES − A ⋅ ER ) IR = 243.45824 − 85.51073j A IR = 258.03875 A arg ( IR) = −19.35299 deg ⎯ SR := 3 ⋅ ER ⋅ IR SR = 59.03549 + 20.73525j MVA SR = 62.57107 MVA arg ( SR) = 19.35299 deg IS := C ⋅ ER + D ⋅ IR IS = 226.12029 + 76.75506j A IS = 238.79222 A arg ( IS ) = 18.74945 deg ⎯ SS := 3 ⋅ ES ⋅ IS SS = 61.61008 − 7.29143j MVA SS = 62.04004 MVA arg ( SS ) = −6.74945 deg SL := SS − SR SL = 2.57459 − 28.02668j MVA SL = 28.14468 MVA arg ( SL) = −84.75142 deg IR := B ΘΕΜΑ 3ο (3 βαθµοί) MVA := 1000kW MW := MVA f := 50 ⋅ Hz ω := 2πf ω = 314.15927 Hz MVAr := MVA X := 80Ω PR := 2345.653MW PR := 2300MW V := 400 ⋅ ( kV) ⋅ e j⋅ 0 V = 230.94011 kV (nominal phase voltage) 3 Ερώτηµα (α) Bcmax := 1.7 ⋅ 10 −2 mho ⎛ ⎝ Pmax_ideal_1circuits := 1 ⋅ ⎜ 3 ⋅ ⎞ X ⎠ 2 2⋅V Pmax_ideal_1circuits = 4000 MW Pmax_ideal_2circuits := 2 ⋅ Pmax_ideal_1circuits ⎡ ⎢ ⎢ ⎣ Pmax_SVC_1circuits := 1 ⋅ ⎢ 3 ⋅ ⎤ ⎥ X ⋅ Bcmax ⎞ ⎥ ⎛ X ⋅ ⎜1 − 4 ⎝ ⎠⎥ ⎦ Pmax_ideal_2circuits = 8000 MW 2 V (για δ=900) (οριακή ευστάθεια Pmax_SVC_1circuits = 3030.30303 MW Pmax_SVC_2circuits := 2 ⋅ Pmax_SVC_1circuits ⎛ ⎝ δ A := 2 acos⎜ 1 − X ⋅ Bcmax ⎞ 4 Pmax_SVC_2circuits = 6060.60606 MW δ A = 97.40025 deg ⎠ δA > π 2 ( ) Pmax_1circuits = 3005.0624 MW Pmax_2circuits := Pmax_SVC_2circuits ⋅ sin δ A ( ) Pmax_2circuits = 6010.12479 MW Pmax_2circuits := 2 ⋅ Pmax_1circuits Pmax_2circuits = 6010.12479 MW Pmax_1circuits := Pmax_SVC_1circuits ⋅ sin δ A ⎛ δA ⎞ ⎝2⎠ Pmax_1circuits = 3005.0624 MW ⎛ δA ⎞ ⎝2⎠ Pmax_2circuits = 6010.12479 MW Pmax_1circuits := Pmax_ideal_1circuits ⋅ sin⎜ Pmax_2circuits := Pmax_ideal_2circuits ⋅ sin⎜ Ερώτηµα (β) ⎛ PR δ 1 := 2 asin⎜ ⎞ δ 1 = 33.41669 deg ⎝ Pmax_ideal_2circuits ⎠ ⎛ PR δ 2 := 2 asin⎜ ⎞ δ 2 = 70.19926 deg ⎝ Pmax_ideal_1circuits ⎠ ( E1 := PR ⋅ δ 2 − δ 1 ) δ2 ⌠ ⎛ δ ⎞ dδ − Pmax_ideal_1circuits ⋅ ⎮ sin⎜ ⎮ ⎝2⎠ ⌡δ 1 δ2 < δA ( E2A := −PR ⋅ δ A − δ 2 ) δA ⌠ + Pmax_ideal_1circuits ⋅ ⎮ ⎮ ⌡δ ⎛ δ ⎞ dδ ⎝2⎠ sin⎜ 2 E1 = 359.52944 MW ⎛ ⎞ PR δ 3 := asin⎜ δ 3 = 49.37612 deg ⎝ Pmax_SVC_1circuits ⎠ δ crit := π − δ 3 δ crit = 130.62388 deg δ crit ⌠ E2B := −PR ⋅ δ crit − δ A + Pmax_SVC_1circuits ⋅ ⎮ ⌡δ ( ) δ crit ⌠ E2B := −PR ⋅ δ crit − δ A + Pmax_SVC_1circuits ⋅ ⎮ ⌡δ ( ) sin( δ ) dδ A sin( δ ) dδ A E1 = 359.52944 MW E2A = 173.30955 MW E2 := E2A + E2B E2B = 249.01702 MW E2 = 422.32657 MW E2 − E1 = 62.79713 MW ...
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This note was uploaded on 10/02/2009 for the course G 001 taught by Professor Shmmygr during the Spring '07 term at National Technical University of Athens, Athens.

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